Question

[6 points] Find the volume of the solid obtained when the region bounded by $y = x^2$ and $y = x^4$ in the first quadrant $(x > 0)$, is revolved about the y-axis.

Name: [6 points] Find the volume of the solid obtained when the region bounded by y = x^2 and y = x^4 in the first quadrant (x > 0), is revolved about the y-axis.
Uploaded: 2022-08-29T12:26:54-08:00
Duration: 2 min 39 s
Channel: Ma. Theresa Alin
Description: [6 points] Find the volume of the solid obtained when the region bounded by y = x^2 and y = x^4 in the first quadrant (x > 0), is revolved about the y-axis.

          [6 points] Find the volume of the solid obtained when the region bounded by \(y = x^2\) and \(y = x^4\) in the first quadrant \((x > 0)\), is revolved about the y-axis.

Added by Enrique C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

08/29/2022

Step 1

$x^2 = x^4$ $x^4 - x^2 = 0$ $x^2(x^2 - 1) = 0$ $x^2 = 0$ or $x^2 - 1 = 0$ $x = 0$ or $x = 1$ or $x = -1$ Since we are in the first quadrant, we only consider $x = 0$ and $x = 1$. Show more…

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[6 points] Find the volume of the solid obtained when the region bounded by $y = x^2$ and $y = x^4$ in the first quadrant ($x > 0$), is revolved about the y-axis.